Orthogonal Frequency Division Multiplexing (OFDM), a method of encoding digital data on multiple carrier frequencies, is commonly used for multi-carrier modulation and has found use in applications such as digital television and audio broadcasting, DSL internet access, wireless networks, power line networks, and 4G mobile communications. Over the years, OFDM has become a standard for wireless communications.
OFDM systems use numerous, closely-spaced, orthogonal sub-carrier signals with overlapping spectra to carry data, with modulation based on Fast Fourier Transform algorithms. OFDM systems use these multiple subcarriers to transmit multiple symbols simultaneously. Where multiplexing is desired or required, OFDM provides several advantages over competing technologies, including a resistance to narrowband fading and relatively high information transmission rates.
OFDM systems, however, have inherently high peak-to-average power ratios (PAPRs), which is caused by constructive interference of sub-tones. More specifically, by the central limit theorem, the addition of many subcarriers produces a Gaussian distributed signal and a corresponding Rayleigh-distributed signal amplitude distribution. The long tail of the Rayleigh amplitude distribution causes power amplifier saturation, which induces signal distortion and degrades demodulation performance at the receiver, thereby reducing the effectiveness and efficiency of the communications system.
Over the years, many approaches have been developed to mitigate the PAPR problem. Among these approaches, companding offers a computationally-efficient, simple, and effective solution. Companding involves reducing the dynamic range of a signal using a compander. Companders used in OFDM applications are weighting functions that modify an OFDM signal amplitude to reduce the large values resulting from multi-tone constructive interference. Companders simultaneously keep the average power constant by upweighting smaller amplitude values, thereby reducing the PAPR.
Early solutions used companders adapted from audio and speech processing, including μ-law and A-law companders, which have recently been extended to provide better performance. Subsequently, companders were developed by directly modifying the signal amplitude, by using, for example, piecewise linear components, hyperbolic functions, and Airy functions. More recently, compander design has been performed by transforming part or all of the Rayleigh amplitude distribution into a form that is more favorable. These approaches include transformation into a uniform distribution, trapezoidal, linear, inverse square-root, or exponential.
Most recently, compander design has included the use of piecewise linear components, using a constrained optimization approach, to optimally capture the Rayleigh probability density function. These designs demonstrate significantly improved out-of-band power rejection, while simultaneously providing equivalent demodulation performance, at the cost of reduced PAPR reduction performance.
What is needed, therefore, is a more generalized version of the constrained optimization approach described above that alleviates assumptions on the parametric form of the approximating function, thereby providing additional flexibility for compander design, which may be taken advantage of to provide one or all of enhanced PAPR performance (i.e. a reduced PAPR), reduced out-of-band power, and/or improved demodulation performance.